Voting on relations using pairs information (Michael Orrison, HMC)

Many aggregation problems ask us to turn individual judgments into a single collective outcome. In this talk, we model each voter’s input as a relation on a set of alternatives, allowing pairwise comparisons to include strict preferences, ties, or incomparability. This perspective gives a common framework for median procedures and scoring methods, including several familiar voting rules. The distance-based side leads naturally to graphs such as the hypercube of relations, while the scoring-based side leads to questions about linear operators on functions on relations. At the center is a natural four-parameter family of scoring matrices whose eigenspace decompositions separate meaningful types of pairwise information, connecting voting theory with graph theory, linear algebra, and harmonic analysis.

This is joint work with Karl-Dieter Crisman, Erin McNicholas, and Kathryn Nyman.